A conjectured upper bound on the Choptuik critical exponents

Abstract

Near-critical type II gravitational collapse is characterized by the formation of arbitrarily small black holes whose horizon radii are described by the simple scaling law rBH∝(p−p⁎)γ, where γ is the matter-dependent Choptuik critical exponent and Δp≡p−p⁎ is the phase space distance from the exact self-similar critical evolution. We point out that all matter models studied thus far in the physics literature are characterized by the upper bound γ≤1. We conjecture that this is a generic feature of non-linear gravitational collapse scenarios.